Problem: Rewrite as a simplified fraction. ${2.2\overline{30} = {?}}$
Explanation: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 2230.303...\\ 10x &= 22.303...\end{align*}}$ Subtracting the two equations, we have: ${990x = 2208}$ ${x = \dfrac{2208}{990}} $ ${x = \dfrac{368}{165}} \text{or} {2 \dfrac{38}{165}}$